Well-defined sets

Hi! I tried to answer this question. Could you please tell me if I answered it correctly? I answered no, because we do not know exactly which persons are smokers, have a health problem, or is a male.Thank you.

Let U = {xlx is an American}
C = {xlx is a smoker}
D = {xlx has a health problem}
E = {xlx is a male}

In order that a set be well defined, we must be able, theoretically, to determine whether or not any given object is in the set. We could, certainly, given an specific person, test the DNA of that person to determine whether or not that person is male. Similarly, any given person either is or is not a smoker. Whether we know which or not is not relevant. I will concede that "health problem" might be sufficiently vague that the set might not be well defined.